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Search: id:A126949
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| A126949 |
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Moduli n for which -1 is a power residue for some power greater than 2: i.e. m^k == -1 mod n for some k>1 and some m>1. |
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+0
1
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| 5, 7, 9, 10, 11, 13, 14, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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A. Amiot, About autosimilar melodies.
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EXAMPLE
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19 is in the sequence because -1 == 10^9 mod 19.
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MATHEMATICA
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ord[x_, n_] := Module[{k = 1}, While[k <= EulerPhi[n]/2 && PowerMod[x, k, n] != n - 1, k++ ]; If[PowerMod[x, k, n] == n - 1, k, infinity]] iGeneralise[n_] := Module[{candidats = Range[n - 2]}, candidats = Select[candidats, (GCD[n, # ] == 1) &]; Select[candidats, (ord[ #, n] < n) &] ] sol = {}; Do[If[iGeneralise[n] != {}, AppendTo[sol, n]], {n, 2, 100}]
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CROSSREFS
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Cf. A008784.
Sequence in context: A143730 A160811 A116451 this_sequence A079696 A129270 A153031
Adjacent sequences: A126946 A126947 A126948 this_sequence A126950 A126951 A126952
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KEYWORD
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nonn
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AUTHOR
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Emmanuel Amiot (manu.amiot(AT)free.fr), Mar 19 2007
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